Cremona's table of elliptic curves

9648 = 2⁴ · 3² · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 67-	Signs for the Atkin-Lehner involutions
Class	9648n	Isogeny class
Conductor	9648	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-1800548352 = -1 · 212 · 38 · 67	Discriminant
Eigenvalues	2- 3-  0  0 -6  4  7  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,240,1456]	[a1,a2,a3,a4,a6]
j	512000/603	j-invariant
L	1.9859017489629	L(r)(E,1)/r!
Ω	0.99295087448144	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	603d1 38592bq1 3216i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 9648n1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	0	0	-6	4	7	5	-1	-1	4	3	0	6	9	-10	3	2	-	-16	-7	-8	-4	15	4

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Quadratic twists for elliptic curve 9648n1

-4	8	-3
603d1	38592bq1	3216i1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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